Why would you ask such a question? This forum is not to give you a design. It is here for interactive consultation. You should not depend on a forum to design something for you...that's irresponsible. You have given none of the design parameters except that it is to be a monorail beam.
having said that, there are several text books that have solved examples on of which is AISC Design Guide 7: Industrial Buildings--Roofs to Anchor Rods (Second Edition)by Dr. James Fisher. Additional resources and references are as follows:
1. American National Standards Institute (ANSI): MH27.1 - "Underhung Cranes and Monorail Systems"
2. American Institute of Steel Construction (AISC) 9th Edition Allowable Stress Design (ASD) Manual (1989)
3. Allowable Bending Stresses for Overhanging Monorails" - by N. Stephen Tanner - AISC Engineering Journal (3rd Quarter, 1985)
4. Crane Manufacturers Association of America, Inc. (CMAA) - Publication No. 74 - "Specifications for Top Running & Under Running Single Girder Electric Traveling Cranes Utilizing Under Running Trolley Hoist" (2004)
5. Design of Monorail Systems" - by Thomas H. Orihuela Jr., PE (
You need to account for impact loading, gravity load, trolley, hoist and chain bucket weights, lateral loading. Special attention must be paid if you have a cantilever and what effective length to use. There are several schools of thought on this one. Local stresses in teh beam flange are critical as well.
